This mini-lesson covers Topic 9 of Edexcel A-level Mathematics (9MA0): moments in static contexts. You will find the moment of a force (including a force acting at an angle), use the two conditions for the equilibrium of a rigid body, work with uniform and non-uniform rods on supports, and solve tilting problems. Take g = 9.8 m s⁻².
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Throughout, take g = 9.8 m s−2 unless a question says otherwise. Press Start when you are ready.
A moment is the turning effect of a force about a point.
A force of 30 N acts perpendicular to a rod, 0.6 m from the pivot.
Moment = 30 × 0.6 = 18 N m.
Now suppose a 20 N force acts 3 m from the pivot at 40° to the rod:
Moment = F d sin θ = 20 × 3 × sin 40° = 60 × 0.6428 = 38.6 N m (3 s.f.)
A rigid body in equilibrium needs two conditions, not one:
The weight of a uniform rod acts at its midpoint (its centre of mass). For a non-uniform rod, the centre of mass is somewhere else — and finding it is often the question.
A uniform beam is pivoted at its midpoint. A 30 N weight sits 1.5 m to the left of the pivot. Where must a 45 N weight sit on the right to balance it?
Anticlockwise = clockwise: 30 × 1.5 = 45 × d → 45 = 45d → d = 1 m from the pivot.
(The beam's own weight acts at the pivot, so it has zero moment about it and can be ignored here.)
The key tactic: if there are two unknown reactions, take moments about one of them. That reaction has zero moment about its own point of action, so it vanishes and you are left with one unknown.
Tap a statement, then tap where it belongs.
A uniform rod AB of length 4 m and mass 6 kg rests horizontally on supports at A and at C, where AC = 3 m.
Weight = 6 × 9.8 = 58.8 N, acting at the midpoint, 2 m from A.
Moments about A (this kills RA): RC × 3 = 58.8 × 2 → RC = 117.6 ÷ 3 = 39.2 N
Resolving vertically: RA + RC = 58.8 → RA = 58.8 − 39.2 = 19.6 N
Check by taking moments about C: RA × 3 = 58.8 × 1 → RA = 19.6 ✔
Always check. Taking moments about a second point is a free, independent check of both reactions — and the support nearer the centre of mass always carries more.
If a rod is not uniform, its weight does not act at the midpoint. Let the centre of mass be a distance d from one end and solve for d.
A non-uniform rod AB of length 5 m and mass 8 kg rests on supports at A and B. The reaction at A is 30 N. Find the distance of the centre of mass from A.
Weight = 8 × 9.8 = 78.4 N. Resolving vertically: RA + RB = 78.4 → RB = 78.4 − 30 = 48.4 N.
Moments about A: 78.4 × d = RB × 5 = 48.4 × 5 = 242
d = 242 ÷ 78.4 = 3.09 m (3 s.f.) from A — past the midpoint, towards B, as you would expect since RB > RA.
Sense check: the centre of mass always lies nearer the support with the larger reaction. If your answer disagrees, re-check the moments.
When a plank on two supports is on the point of tilting about one support, it is about to lift off the other one — so the reaction at that other support becomes zero. This single fact solves every tilting problem.
A uniform plank AB of length 6 m and mass 20 kg rests on supports at C (1 m from A) and D (4 m from A). A child of mass 30 kg walks from A towards B. How far from A is the child when the plank is about to tilt about D?
About to tilt about D ⇒ RC = 0. The plank's weight (20g) acts at the midpoint, 3 m from A — that is 1 m to the left of D. Let the child be x m from A, so (x − 4) m to the right of D.
Moments about D: 30g × (x − 4) = 20g × 1
The g cancels: 30(x − 4) = 20 → x − 4 = 20 ÷ 30 = 0.667 → x = 4.67 m (3 s.f.) from A.
Take moments about the support it is turning about — then the zero reaction and the pivot reaction both disappear at once, leaving a single equation.
Tap an item on the left, then its partner on the right.
Moment = F × perpendicular distance, in N m — state clockwise or anticlockwise
At an angle: moment = F d sin θ · a force through the point has zero moment
Equilibrium of a rigid body: resultant force = 0 and total moment about any point = 0
Uniform rod: the weight acts at the midpoint · non-uniform: solve for the centre of mass
Tactic: take moments about an unknown reaction to eliminate it
Tilting: about to tilt about one support ⇒ the reaction at the other support is zero
That is the whole of 9MA0 Topic 9 — Moments. Press Finish to see your score.
You have worked through Moments for Edexcel A-level Mathematics (9MA0). 🎉
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Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.